Extended family of generalized Chaplygin gas models

V. M. C. Ferreira; P. P. Avelino

doi:10.1103/PhysRevD.98.043515

paper

Extended family of generalized Chaplygin gas models

arXiv:1807.04656 · doi:10.1103/PhysRevD.98.043515

Abstract

The generalized Chaplygin gas is usually defined as a barotropic perfect fluid with an equation of state $p = - A ρ^{- α}$ , where $ρ$ and $p$ are the proper energy density and pressure, respectively, and $A$ and $α$ are positive real parameters. It has been extensively studied in the literature as a quartessence prototype unifying dark matter and dark energy. Here, we consider an extended family of generalized Chaplygin gas models parameterized by three positive real parameters $A$ , $α$ and $β$ , which, for two specific choices of $β$ [ $β = 1$ and $β = (1 + α) / (2 α)$ ], is described by two different Lagrangians previously identified in the literature with the generalized Chaplygin gas. We show that, for $β > 1/2$ , the linear stability conditions and the maximum value of the sound speed $c_{s}$ are regulated solely by $β$ , with $0 \leq c_{s} \leq 1$ if $β \geq 1$ . We further demonstrate that in the non-relativistic regime the standard equation of state $p = - A ρ^{- α}$ of the generalized Chaplygin gas is always recovered, while in the relativistic regime this is true only if $β = (1 + α) / (2 α)$ . We present a regularization of the ( $α \to 0$ , $A \to \infty$ ) limit of the generalized Chaplygin gas, showing that it leads to a logarithmic Chaplygin gas model with an equation of state of the form $p = A ln (ρ / ρ_{*})$ , where $A$ is a real parameter and $ρ_{*} > 0$ is an arbitrary energy density. We finally derive its Lagrangian formulation.

arXiv comment5 pages

Extended family of generalized Chaplygin gas models

Abstract

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